Abstract

Computer-generated phase gratings (CGPG) have been proposed for optical interconnection schemes to provide source fan-out to output locations.¹ Fan-out is achieved using the CGPG in the Fourier plane of an imaging system to produce a point-spread function having many output spots in some interconnection pattern. A computer is used to design a phase grating function whose power spectrum is the desired connection pattern. The Dammann grating is one example of a binary CGPG commonly used for generating 2-D N×N arrays of uniform intensity beams for optical powering.² Other papers have shown that arbitrary 2-D patterns can be created.³ The Dammann grating is a periodic function so that the optical Fourier transform can be approximated by its Fourier series coefficients. The grating function is found by setting each Fourier series coefficient to a nonzero value for a connection or zero for no connection, and then numerically solving for the periodic binary function that satisfies these Fourier coefficients. However, for large array sizes the computing complexity becomes extreme. A computationally easy way to create CGPG for some specific interconnection pattern is based on the Gerchberg-Saxton algorithm. The interconnection pattern is represented as a function having values of one or zero, corresponding to the desired connection pattern, with arbitrary phase. The task is to find a phase-only grating function whose power spectrum resembles this interconnection function. The desired phase grating function is found by iteratively Fourier transforming the grating function and modifying the phase of the interconnection function until the desired values of on/off ratio, connection uniformity, and/or diffraction efficiency are achieved. The cellular hypercube interconnection⁴ is the main pattern discussed with some generalization to other types of interconnection pattern. Implementation of these CGPG for interconnecting processor arrays is also discussed.

© 1991 Optical Society of America